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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.linear_model</span></code>.ARDRegression</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-linear-model-ardregression">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.linear_model.ARDRegression</span></code></a></li>
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  <div class="section" id="sklearn-linear-model-ardregression">
<h1><a class="reference internal" href="../classes.html#module-sklearn.linear_model" title="sklearn.linear_model"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.linear_model</span></code></a>.ARDRegression<a class="headerlink" href="#sklearn-linear-model-ardregression" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.linear_model.ARDRegression">
<em class="property">class </em><code class="sig-prename descclassname">sklearn.linear_model.</code><code class="sig-name descname">ARDRegression</code><span class="sig-paren">(</span><em class="sig-param">n_iter=300</em>, <em class="sig-param">tol=0.001</em>, <em class="sig-param">alpha_1=1e-06</em>, <em class="sig-param">alpha_2=1e-06</em>, <em class="sig-param">lambda_1=1e-06</em>, <em class="sig-param">lambda_2=1e-06</em>, <em class="sig-param">compute_score=False</em>, <em class="sig-param">threshold_lambda=10000.0</em>, <em class="sig-param">fit_intercept=True</em>, <em class="sig-param">normalize=False</em>, <em class="sig-param">copy_X=True</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/linear_model/_bayes.py#L384"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.linear_model.ARDRegression" title="Permalink to this definition">¶</a></dt>
<dd><p>Bayesian ARD regression.</p>
<p>Fit the weights of a regression model, using an ARD prior. The weights of
the regression model are assumed to be in Gaussian distributions.
Also estimate the parameters lambda (precisions of the distributions of the
weights) and alpha (precision of the distribution of the noise).
The estimation is done by an iterative procedures (Evidence Maximization)</p>
<p>Read more in the <a class="reference internal" href="../linear_model.html#bayesian-regression"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>n_iter</strong><span class="classifier">int, default=300</span></dt><dd><p>Maximum number of iterations.</p>
</dd>
<dt><strong>tol</strong><span class="classifier">float, default=1e-3</span></dt><dd><p>Stop the algorithm if w has converged.</p>
</dd>
<dt><strong>alpha_1</strong><span class="classifier">float, default=1e-6</span></dt><dd><p>Hyper-parameter : shape parameter for the Gamma distribution prior
over the alpha parameter.</p>
</dd>
<dt><strong>alpha_2</strong><span class="classifier">float, default=1e-6</span></dt><dd><p>Hyper-parameter : inverse scale parameter (rate parameter) for the
Gamma distribution prior over the alpha parameter.</p>
</dd>
<dt><strong>lambda_1</strong><span class="classifier">float, default=1e-6</span></dt><dd><p>Hyper-parameter : shape parameter for the Gamma distribution prior
over the lambda parameter.</p>
</dd>
<dt><strong>lambda_2</strong><span class="classifier">float, default=1e-6</span></dt><dd><p>Hyper-parameter : inverse scale parameter (rate parameter) for the
Gamma distribution prior over the lambda parameter.</p>
</dd>
<dt><strong>compute_score</strong><span class="classifier">bool, default=False</span></dt><dd><p>If True, compute the objective function at each step of the model.</p>
</dd>
<dt><strong>threshold_lambda</strong><span class="classifier">float, default=10 000</span></dt><dd><p>threshold for removing (pruning) weights with high precision from
the computation.</p>
</dd>
<dt><strong>fit_intercept</strong><span class="classifier">bool, default=True</span></dt><dd><p>whether to calculate the intercept for this model. If set
to false, no intercept will be used in calculations
(i.e. data is expected to be centered).</p>
</dd>
<dt><strong>normalize</strong><span class="classifier">bool, default=False</span></dt><dd><p>This parameter is ignored when <code class="docutils literal notranslate"><span class="pre">fit_intercept</span></code> is set to False.
If True, the regressors X will be normalized before regression by
subtracting the mean and dividing by the l2-norm.
If you wish to standardize, please use
<a class="reference internal" href="sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.preprocessing.StandardScaler</span></code></a> before calling <code class="docutils literal notranslate"><span class="pre">fit</span></code>
on an estimator with <code class="docutils literal notranslate"><span class="pre">normalize=False</span></code>.</p>
</dd>
<dt><strong>copy_X</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, X will be copied; else, it may be overwritten.</p>
</dd>
<dt><strong>verbose</strong><span class="classifier">bool, default=False</span></dt><dd><p>Verbose mode when fitting the model.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>coef_</strong><span class="classifier">array-like of shape (n_features,)</span></dt><dd><p>Coefficients of the regression model (mean of distribution)</p>
</dd>
<dt><strong>alpha_</strong><span class="classifier">float</span></dt><dd><p>estimated precision of the noise.</p>
</dd>
<dt><strong>lambda_</strong><span class="classifier">array-like of shape (n_features,)</span></dt><dd><p>estimated precisions of the weights.</p>
</dd>
<dt><strong>sigma_</strong><span class="classifier">array-like of shape (n_features, n_features)</span></dt><dd><p>estimated variance-covariance matrix of the weights</p>
</dd>
<dt><strong>scores_</strong><span class="classifier">float</span></dt><dd><p>if computed, value of the objective function (to be maximized)</p>
</dd>
<dt><strong>intercept_</strong><span class="classifier">float</span></dt><dd><p>Independent term in decision function. Set to 0.0 if
<code class="docutils literal notranslate"><span class="pre">fit_intercept</span> <span class="pre">=</span> <span class="pre">False</span></code>.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>For an example, see <a class="reference internal" href="../../auto_examples/linear_model/plot_ard.html#sphx-glr-auto-examples-linear-model-plot-ard-py"><span class="std std-ref">examples/linear_model/plot_ard.py</span></a>.</p>
<p class="rubric">References</p>
<p>D. J. C. MacKay, Bayesian nonlinear modeling for the prediction
competition, ASHRAE Transactions, 1994.</p>
<p>R. Salakhutdinov, Lecture notes on Statistical Machine Learning,
<a class="reference external" href="http://www.utstat.toronto.edu/~rsalakhu/sta4273/notes/Lecture2.pdf#page=15">http://www.utstat.toronto.edu/~rsalakhu/sta4273/notes/Lecture2.pdf#page=15</a>
Their beta is our <code class="docutils literal notranslate"><span class="pre">self.alpha_</span></code>
Their alpha is our <code class="docutils literal notranslate"><span class="pre">self.lambda_</span></code>
ARD is a little different than the slide: only dimensions/features for
which <code class="docutils literal notranslate"><span class="pre">self.lambda_</span> <span class="pre">&lt;</span> <span class="pre">self.threshold_lambda</span></code> are kept and the rest are
discarded.</p>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">linear_model</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">clf</span> <span class="o">=</span> <span class="n">linear_model</span><span class="o">.</span><span class="n">ARDRegression</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">ARDRegression()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="go">array([1.])</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.linear_model.ARDRegression.fit" title="sklearn.linear_model.ARDRegression.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(self, X, y)</p></td>
<td><p>Fit the ARDRegression model according to the given training data and parameters.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.linear_model.ARDRegression.get_params" title="sklearn.linear_model.ARDRegression.get_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code></a>(self[, deep])</p></td>
<td><p>Get parameters for this estimator.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.linear_model.ARDRegression.predict" title="sklearn.linear_model.ARDRegression.predict"><code class="xref py py-obj docutils literal notranslate"><span class="pre">predict</span></code></a>(self, X[, return_std])</p></td>
<td><p>Predict using the linear model.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.linear_model.ARDRegression.score" title="sklearn.linear_model.ARDRegression.score"><code class="xref py py-obj docutils literal notranslate"><span class="pre">score</span></code></a>(self, X, y[, sample_weight])</p></td>
<td><p>Return the coefficient of determination R^2 of the prediction.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.linear_model.ARDRegression.set_params" title="sklearn.linear_model.ARDRegression.set_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code></a>(self, \*\*params)</p></td>
<td><p>Set the parameters of this estimator.</p></td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="sklearn.linear_model.ARDRegression.__init__">
<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">n_iter=300</em>, <em class="sig-param">tol=0.001</em>, <em class="sig-param">alpha_1=1e-06</em>, <em class="sig-param">alpha_2=1e-06</em>, <em class="sig-param">lambda_1=1e-06</em>, <em class="sig-param">lambda_2=1e-06</em>, <em class="sig-param">compute_score=False</em>, <em class="sig-param">threshold_lambda=10000.0</em>, <em class="sig-param">fit_intercept=True</em>, <em class="sig-param">normalize=False</em>, <em class="sig-param">copy_X=True</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/linear_model/_bayes.py#L494"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.linear_model.ARDRegression.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>Initialize self.  See help(type(self)) for accurate signature.</p>
</dd></dl>

<dl class="method">
<dt id="sklearn.linear_model.ARDRegression.fit">
<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/linear_model/_bayes.py#L511"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.linear_model.ARDRegression.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit the ARDRegression model according to the given training data
and parameters.</p>
<p>Iterative procedure to maximize the evidence</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Training vector, where n_samples in the number of samples and
n_features is the number of features.</p>
</dd>
<dt><strong>y</strong><span class="classifier">array-like of shape (n_samples,)</span></dt><dd><p>Target values (integers). Will be cast to X’s dtype if necessary</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">returns an instance of self.</span></dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.linear_model.ARDRegression.get_params">
<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L173"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.linear_model.ARDRegression.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">mapping of string to any</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.linear_model.ARDRegression.predict">
<code class="sig-name descname">predict</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">return_std=False</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/linear_model/_bayes.py#L620"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.linear_model.ARDRegression.predict" title="Permalink to this definition">¶</a></dt>
<dd><p>Predict using the linear model.</p>
<p>In addition to the mean of the predictive distribution, also its
standard deviation can be returned.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>Samples.</p>
</dd>
<dt><strong>return_std</strong><span class="classifier">bool, default=False</span></dt><dd><p>Whether to return the standard deviation of posterior prediction.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>y_mean</strong><span class="classifier">array-like of shape (n_samples,)</span></dt><dd><p>Mean of predictive distribution of query points.</p>
</dd>
<dt><strong>y_std</strong><span class="classifier">array-like of shape (n_samples,)</span></dt><dd><p>Standard deviation of predictive distribution of query points.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.linear_model.ARDRegression.score">
<code class="sig-name descname">score</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y</em>, <em class="sig-param">sample_weight=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L376"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.linear_model.ARDRegression.score" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the coefficient of determination R^2 of the prediction.</p>
<p>The coefficient R^2 is defined as (1 - u/v), where u is the residual
sum of squares ((y_true - y_pred) ** 2).sum() and v is the total
sum of squares ((y_true - y_true.mean()) ** 2).sum().
The best possible score is 1.0 and it can be negative (because the
model can be arbitrarily worse). A constant model that always
predicts the expected value of y, disregarding the input features,
would get a R^2 score of 0.0.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Test samples. For some estimators this may be a
precomputed kernel matrix or a list of generic objects instead,
shape = (n_samples, n_samples_fitted),
where n_samples_fitted is the number of
samples used in the fitting for the estimator.</p>
</dd>
<dt><strong>y</strong><span class="classifier">array-like of shape (n_samples,) or (n_samples, n_outputs)</span></dt><dd><p>True values for X.</p>
</dd>
<dt><strong>sample_weight</strong><span class="classifier">array-like of shape (n_samples,), default=None</span></dt><dd><p>Sample weights.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>score</strong><span class="classifier">float</span></dt><dd><p>R^2 of self.predict(X) wrt. y.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The R2 score used when calling <code class="docutils literal notranslate"><span class="pre">score</span></code> on a regressor will use
<code class="docutils literal notranslate"><span class="pre">multioutput='uniform_average'</span></code> from version 0.23 to keep consistent
with <a class="reference internal" href="sklearn.metrics.r2_score.html#sklearn.metrics.r2_score" title="sklearn.metrics.r2_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">r2_score</span></code></a>. This will influence the
<code class="docutils literal notranslate"><span class="pre">score</span></code> method of all the multioutput regressors (except for
<a class="reference internal" href="sklearn.multioutput.MultiOutputRegressor.html#sklearn.multioutput.MultiOutputRegressor" title="sklearn.multioutput.MultiOutputRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">MultiOutputRegressor</span></code></a>). To specify the
default value manually and avoid the warning, please either call
<a class="reference internal" href="sklearn.metrics.r2_score.html#sklearn.metrics.r2_score" title="sklearn.metrics.r2_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">r2_score</span></code></a> directly or make a custom scorer with
<a class="reference internal" href="sklearn.metrics.make_scorer.html#sklearn.metrics.make_scorer" title="sklearn.metrics.make_scorer"><code class="xref py py-func docutils literal notranslate"><span class="pre">make_scorer</span></code></a> (the built-in scorer <code class="docutils literal notranslate"><span class="pre">'r2'</span></code> uses
<code class="docutils literal notranslate"><span class="pre">multioutput='uniform_average'</span></code>).</p>
</dd></dl>

<dl class="method">
<dt id="sklearn.linear_model.ARDRegression.set_params">
<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">**params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L205"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.linear_model.ARDRegression.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as pipelines). The latter have parameters of the form
<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
component of a nested object.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

</dd></dl>

<div class="section" id="examples-using-sklearn-linear-model-ardregression">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.linear_model.ARDRegression</span></code><a class="headerlink" href="#examples-using-sklearn-linear-model-ardregression" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="Fit regression model with Bayesian Ridge Regression."><div class="figure align-default" id="id1">
<img alt="../../_images/sphx_glr_plot_ard_thumb.png" src="../../_images/sphx_glr_plot_ard_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/linear_model/plot_ard.html#sphx-glr-auto-examples-linear-model-plot-ard-py"><span class="std std-ref">Automatic Relevance Determination Regression (ARD)</span></a></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
</div>
</div><div class="clearer"></div></div>
</div>


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